Robust Stabilization of Inverted Pendulum Using ALQR Augmented by Second-Order Sliding Mode Control

In this paper, a robust nonlinear control design strategy to solve the stabilization problem of an inverted pendulum system subject to parametric uncertainties and unmodeled dynamics is proposed. The control strategy is based on the combination of Amplified Linear Quadratic Regulator (ALQR) control with a high-order sliding mode algorithm. Differently from the standard ALQR controller, parametric uncertainties are considered in the design process. Linear matrix inequality conditions are provided to deal with the computational issues arising with the inclusion of this feature. A sliding mode term is added to the ALQR control law to mitigate the effect of unmodeled dynamics, such as dry friction, neglected in the system model. In order to prevent the occurrence of chattering, a high-order sliding mode approach was used, namely the second-order super-twisting algorithm. The effectiveness of the proposed strategy is evaluated through a real experiment performed using the Quanser inverted pendulum plant. © 2017, Brazilian Society for Automatics--SBA.